The purpose of this study is to determine the effectiveness of different doses of epoetin alfa for treating anemia in patients who have cancer; or patients who no longer have any signs of cancer, but remain anemic as a result of their treatment. These patients should not be currently receiving chemotherapy or radiotherapy. A subject's participation in the study will last approximately 6 months. Subjects will receive weekly doses of epoetin alfa or placebo. Their hemoglobin will be tested every week.